Theory and Practice of Uncertain Programming
Real-life decisions are usually made in the state of uncertainty (randomness, fuzziness, roughness, etc.). How do we model optimization problems in uncertain environments? How do we solve these models? In order to answer these questions, this book provide
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Studies in Fuzziness and Soft Computing Editor-in-chief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw, Poland E-mail: [email protected] http://www.springer.de/cgi-bin/search_book.pl?series = 2941
Further volumes of this series can be found at our homepage. Vol. 81. V. Dimitrov and V. Korotkich (Eds.) Fuzzy Logic, 2002 ISBN 3-7908-1425-3 Vol. 82. Ch. Carlsson and R. Fullr Fuzzy Reasoning in Decision Making and Optimization, 2002 ISBN 3-7908-1428-8 Vol. 83. S. Barro and R. MarÌn (Eds.) Fuzzy Logic in Medicine, 2002 ISBN 3-7908-1429-6 Vol. 84. L. C. Jain and J. Kacprzyk (Eds.) New Learning Paradigms in Soft Computing, 2002 ISBN 3-7908-1436-9 Vol. 85. D. Rutkowska Neuro-Fuzzy Architectures and Hybrid Learning, 2002 ISBN 3-7908-1438-5 Vol. 86. M. B. Gorzaøczany Computational Intelligence Systems and Applications, 2002 ISBN 3-7908-1439-3 Vol. 87. C. Bertoluzza, M. . Gil and D. A. Ralescu (Eds.) Statistical Modeling, Analysis and Management of Fuzzy Data, 2002 ISBN 3-7908-1440-7 Vol. 88. R. P. Srivastava and T. J. Mock (Eds.) Belief Functions in Business Decisions, 2002 ISBN 3-7908-1451-2 Vol. 89. B. Bouchon-Meunier, J. Gutirrez-RÌos, L. Magdalena and R. R. Yager (Eds.) Technologies for Constructing Intelligent Systems 1, 2002 ISBN 3-7908-1454-7 Vol. 90. B. Bouchon-Meunier, J. Gutirrez-RÌos, L. Magdalena and R. R. Yager (Eds.) Technologies for Constructing Intelligent Systems 2, 2002 ISBN 3-7908-1455-5
Vol. 91. J. J. Buckley, E. Eslami and T. Feuring Fuzzy Mathematics in Economics and Engineering, 2002 ISBN 3-7908-1456-3 Vol. 92. P. P. Angelov Evolving Rule-Based Models, 2002 ISBN 3-7908-1457-1 Vol. 93. V. V. Cross and T. A. Sudkamp Similarity and Compatibility in Fuzzy Set Theory, 2002 ISBN 3-7908-1458-X Vol. 94. M. MacCrimmon and P. Tillers (Eds.) The Dynamics of Judicial Proof, 2002 ISBN 3-7908-1459-8 Vol. 95. T. Y. Lin, Y. Y. Yao and L. A. Zadeh (Eds.) Data Mining, Rough Sets and Granular Computing, 2002 ISBN 3-7908-1461-X Vol. 96. M. Schmitt, H.-N. Teodorescu, A. Jain, A. Jain, S. Jain and L. C. Jain (Eds.) Computational Intelligence Processing in Medical Diagnosis, 2002 ISBN 3-7908-1463-6 Vol. 97. T. Calvo, G. Mayor and R. Mesiar (Eds.) Aggregation Operators, 2002 ISBN 3-7908-1468-7 Vol. 98. L. C. Jain, Z. Chen and N. Ichalkaranje (Eds.) Intelligent Agents and Their Applications, 2002 ISBN 3-7908-1469-5 Vol. 99. C. Huang and Y. Shi Towards Efficient Fuzzy Information Processing, 2002 ISBN 3-7908-1475-X Vol. 100. S.-H. Chen (Ed.) Evolutionary Computation in Economics and Finance, 2002 ISBN 3-7908-1476-8 Vol. 101. S. J. Ovaska and L. M. Sztandera (Eds.) Soft Computing in Industrial Electronics, 2002 ISBN 3-7908-1477-6
Baoding Liu
Theory and Practice of Uncertain Programming With 25 Figures and 13 Tables
Springer-Verlag Berlin Heidelberg GmbH
Professor Baoding Liu Tsinghua University Uncertain Systems Laboratory Department of Mathematical Sciences Beijing 100084 China [email protected]
ISSN 1434-9922 ISBN 978-3-662-13196-1 Liu, Baoding: The
